Rethinking Amortized Neural Representations for High-Resolution Terrain Elevation Data

Implicit neural representations (INRs) model a signal as a continuous coordinate-to-value function. For terrain elevation data, this supports analytic derivatives, arbitrary-resolution decoding, and a smooth surface model of the underlying heightfield. However, fitting and storing a separate INR for every tile does not scale to large terrain datasets. Amortized neural representations reduce this cost with a shared network: a new tile is mapped to a compact per-tile payload, and a shared decoder reconstructs the heightfield from it. Most such methods are hypernetworks that predict the payload in a single forward pass, while others recover it through a short per-tile optimization. These methods were developed primarily for natural images, and their suitability for terrain heightfields remains unclear. We introduce a controlled benchmark on a 1 m/pixel terrain dataset and evaluate three representative methods under a unified protocol. Observing a clear cross-domain gap, we propose HUVR+SIREN, a hypernetwork that adapts the strongest benchmarked method (HUVR) by replacing its coordinate decoder with a smooth, analytically differentiable one. It attains the best height and derivative fidelity on the benchmark with no additional per-tile storage and lower decode cost, and tolerates aggressive post-training quantization with negligible quality loss, giving a compact terrain neural format. Ablations and diagnostics further identify which design choices transfer to terrain and show that the per-tile bottleneck is already near its useful limit, leaving the remaining gap in the shared hypernetwork's architectural design.

ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

SASNet: Spatially-Adaptive Sinusoidal Neural Networks

Sinusoidal neural networks (SNNs) have emerged as powerful implicit neural representations (INRs) for low-dimensional signals in computer vision and graphics. They enable high-frequency signal reconstruction and smooth manifold modeling; however, they often suffer from spectral bias, training instability, and overfitting. To address these challenges, we propose SASNet, Spatially-Adaptive SNNs that robustly enhance the capacity of compact INRs to fit detailed signals. SASNet integrates a frequency embedding layer to control frequency components and mitigate spectral bias, along with jointly optimized, spatially-adaptive masks that localize neuron influence, reducing network redundancy and improving convergence stability. Robust to hyperparameter selection, SASNet faithfully reconstructs high-frequency signals without overfitting low-frequency regions. Our experiments show that SASNet outperforms state-of-the-art INRs, achieving strong fitting accuracy, super-resolution capability, and noise suppression, without sacrificing model compactness.

Critical Features Tracking on Triangulated Irregular Networks by a Scale-Space Method

The scale-space method is a well-established framework that constructs a hierarchical representation of an input signal and facilitates coarse-to-fine visual reasoning. Considering the terrain elevation function as the input signal, the scale-space method can identify and track significant topographic features across different scales. The number of scales a feature persists, called its life span, indicates the importance of that feature. In this way, important topographic features of a landscape can be selected, which are useful for many applications, including cartography, nautical charting, and land-use planning. The scale-space methods developed for terrain data use gridded Digital Elevation Models (DEMs) to represent the terrain. However, gridded DEMs lack the flexibility to adapt to the irregular distribution of input data and the varied topological complexity of different regions. Instead, Triangulated Irregular Networks (TINs) can be directly generated from irregularly distributed point clouds and accurately preserve important features. In this work, we introduce a novel scale-space analysis pipeline for TINs, addressing the multiple challenges in extending grid-based scale-space methods to TINs. Our pipeline can efficiently identify and track topologically important features on TINs. Moreover, it is capable of analyzing terrains with irregular boundaries, which poses challenges for grid-based methods. Comprehensive experiments show that, compared to grid-based methods, our TIN-based pipeline is more efficient, accurate, and has better resolution robustness.

ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis

Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth manifolds, the absence of an easy-to-use continuous surface model for a large terrain results in a preference for discrete meshes. Structural representation based on topology provides a succinct surface description, laying the foundation for many terrain analysis applications. However, on discrete meshes, numerical issues emerge, and complex algorithms are designed to handle them. This paper brings the context of terrain data analysis back to the continuous world and introduces ImplicitTerrain (Project homepage available at https://fengyee.github.io/implicit-terrain/), an implicit neural representation (INR) approach for modeling high-resolution terrain continuously and differentiably. Our comprehensive experiments demonstrate superior surface fitting accuracy, effective topological feature retrieval, and various topographical feature extraction that are implemented over this compact representation in parallel. To our knowledge, ImplicitTerrain pioneers a feasible continuous terrain surface modeling pipeline that provides a new research avenue for our community.